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14 miles on the route he took. 10 miles if you mean in a straight line.

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Q: A marathon runner runs 6 miles south and 8 miles east How far is the runner from the starting point?
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(Distance)2 = (6)2 + (8)2 = 36 + 64 = 100Distance = sqrt(100) = 10 milesTo be honest about it, this is only an approximation. The formula used here is only validon a flat surface, and we all know that the earth is a spherical surface.Even worse than that ... the formula is only valid if the two directions are perpendicular (90°)to each other. But north and east are only perpendicular at the equator; the farther you arefrom the equator, the less perpendicular they are.To show you how bad it can get: If you start at the north pole, go 6 miles south,and then go 8 miles east, you wind up only 6 miles from where you started.In order to answer this question accurately, you have to know exactly where on earththe marathon runner started from, and then you have to use spherical trigonometry.I'm sure you'll be happy that I'm not going to do that. It's valid because we don't knowwhere he started from.We'll just say: The answer is "approximately 10 miles", and the closer our runner isto the equator, the more accurate this answer is.


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